Details

sample245.0ms

Algorithm

intervals

Results

80.0ms	80×	body	1280	valid
60.0ms	87×	body	640	valid
59.0ms	265×	body	80	valid
21.0ms	46×	body	320	valid
5.0ms	17×	body	160	valid

simplify298.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

297.0ms

(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize27.0ms

Local error

Found 3 expressions with local error:

4.0b	(- (exp l) (exp (- l)))
0.2b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

Slowest

76.0ms	(* J (- (exp l) (exp (- l))))
67.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
24.0ms	(- (exp l) (exp (- l)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

163.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
72.0ms	(* J (- (exp l) (exp (- l))))
54.0ms	(- (exp l) (exp (- l)))

simplify8.7s

Counts

80 → 108

Calls

80 calls:

Slowest

641.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
315.0ms	(+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))
279.0ms	(* (* J (- (pow (exp l) 3) (pow (exp (- l)) 3))) (cos (/ K 2)))
271.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
266.0ms	(* J (- (exp l) (exp (* -1 l))))

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
0.0b	(* l (fma 1/3 (* l l) 2))
0.0b	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
0.0b	(fma 1/3 (* l l) 2)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

Slowest

19.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
11.0ms	(* l (fma 1/3 (* l l) 2))
11.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
0.0ms	(fma 1/3 (* l l) 2)

series704.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

244.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
230.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
136.0ms	(* l (fma 1/3 (* l l) 2))
94.0ms	(fma 1/3 (* l l) 2)

simplify8.1s

Counts

45 → 90

Calls

45 calls:

Slowest

836.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
732.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
497.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
475.0ms	(sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
469.0ms	(fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
0.1b	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
0.0b	(* l (fma 1/3 (* l l) 2))
0.0b	(fma 1/3 (* l l) 2)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 76

Calls

4 calls:

Slowest

19.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
12.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
10.0ms	(* l (fma 1/3 (* l l) 2))
0.0ms	(fma 1/3 (* l l) 2)

series567.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

250.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
143.0ms	(* l (fma 1/3 (* l l) 2))
106.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
68.0ms	(fma 1/3 (* l l) 2)

simplify7.6s

Counts

43 → 88

Calls

43 calls:

Slowest

884.0ms	(* (* (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
741.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
507.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))
504.0ms	(sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
476.0ms	(+ (log (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (log (cos (/ K 2))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))
0.4b	(* l (sqrt (fma 1/3 (* l l) 2)))
0.1b	(* (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2))))) (cos (/ K 2)))
0.0b	(* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`sqrt-prod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 93

Calls

4 calls:

Slowest

40.0ms	(* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))
16.0ms	(* (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2))))) (cos (/ K 2)))
13.0ms	(* l (sqrt (fma 1/3 (* l l) 2)))
5.0ms	(* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

214.0ms	(* (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2))))) (cos (/ K 2)))
177.0ms	(* l (sqrt (fma 1/3 (* l l) 2)))
172.0ms	(* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))
127.0ms	(* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))

simplify7.1s

Counts

60 → 105

Calls

60 calls:

Slowest

413.0ms	(* (* (* (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2))))) (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))) (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
406.0ms	(fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2))))
361.0ms	(+ (* 1/3 (* J (pow l 3))) (+ (* 2 (* J l)) (* 1/60 (* J (pow l 5)))))
353.0ms	(+ (log (* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))) (log (cos (/ K 2))))
312.0ms	(* J (fma 1/60 (pow l 5) (* (* l (sqrt (fma 1/3 (* l l) 2))) (sqrt (fma 1/3 (* l l) 2)))))

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes360.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.2s	2740×	body	1280	valid
2.5s	2542×	body	640	valid
1.7s	8395×	body	80	valid
1.3s	1466×	body	320	valid
291.0ms	737×	body	160	valid